Path Tracking Control of Unmanned Vehicle Using State Extended Model Predictive Control and Angle Compensation
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摘要: 采用传统模型预测控制(MPC)的无人车难以同时保证路径跟踪精度和实时性,针对此问题,本文设计了一种采用状态扩展MPC与转角补偿的路径跟踪控制器。建立了车辆三自由度动力学模型,设计了基于状态扩展的双反馈MPC控制器,并根据车速调整控制器参数;建立了车辆-道路跟踪模型,根据车辆横向和航向偏差设计了转角补偿模糊控制器;利用MATLAB/Simulink和Carsim软件对所设计的路径跟踪控制器进行联合仿真分析。结果表明:相比采用传统MPC控制器的车辆,在中、低车速下,状态扩展MPC控制器的控制增量求解时间平均值降低14%以上,路径跟踪控制器跟踪道路的横向和航向偏差最大值分别降低23%和17%以上,具有较好的路径跟踪性能。Abstract: It is difficult for an unmanned vehicle to use the traditional model predictive control (MPC) algorithm to ensure path tracking accuracy and real-time performance at the same time. To solve this problem, the paper designs a path tracking controller using the state-extension MPC and angle compensation. A 3-degree-of-freedom vehicle dynamic model is established, a dual-feedback MPC controller based on state extension is designed and the controller's parameters are adjusted according to the unmanned vehicle's speed. The vehicle-road tracking model is established, and the fuzzy controller for angle compensation is designed according to the unmanned vehicle's lateral and heading deviation. The MATLAB/Simulink and Carsim software are used to conduct the joint simulation of the designed path tracking controller. The results show that compared with the traditional MPC controller of an unmanned vehicle, at its medium and low speed, the average time for solving the control increment of the state extension MPC controller is reduced by more than 14% and that the maximum lateral and heading deviation of the path tracking controller is reduced by more than 23% and 17% respectively, thus having a better path tracking performance.
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Key words:
- path tracking /
- state extension /
- model predictive control /
- dual-feedback /
- fuzzy control
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表 1 模糊控制规则表
Table 1. Fuzzy control rule table
ye $ {\varphi _{{e}}} $ NB NM NS ZO PS PM PB NB PB PB PB PB PM PS PS NM PB PB PM PM PS ZO NS NS PB PM PM PS ZO NM NM ZO PM PS PS ZO NS NM NM PS PM PS ZO NS NM NM NB PM PS ZO NM NM NM NB NB PB NS NM NB NB NM NB NB 表 2 整车参数
Table 2. Vehicle parameters
参数 数值 整车质量m/kg 1783 横摆转动惯量Iz /(kg·m2) 4175 前轮侧偏刚度Cf /(N·rad−1) 66900 后轮侧偏刚度Cr /(N·rad−1) 62700 质心距前轴距离a/m 1.232 质心距前轴距离b/m 1.468 路面附着系数µ 1 前轮纵向滑移率sf 0.2 后轮纵向滑移率sr 0.2 表 3 状态扩展MPC控制器参数A
Table 3. State-expanding MPC controller parameters A
参数 数值 离散时间步长T/s 0.05 预测时域Np 10 控制时域Nc 5 输出量误差权重系数矩阵$\bar {\boldsymbol{Q}} $ diag([200,100]) 控制增量权重系数R 5 × 104 表 4 状态扩展MPC控制器参数B
Table 4. State-expanding MPC controller parameters B
参数 数值 离散时间步长T/s 0.05 预测时域Np 12 控制时域Nc 6 输出量误差权重系数矩阵$\bar {\boldsymbol{Q}} $ diag([200,100]) 控制增量权重系数R 1 × 104 表 5 双移线工况控制器控制增量求解时间对比
Table 5. Comparison of control increment solution time for the double-shift-line working condition
车速/(
km·h−1)指标 传统MPC/ms 状态扩展MPC/ms 改善程度/% 36 平均时间 13.56 10.56 22.1 最大时间 32.52 19.15 41.1 54 平均时间 14.88 12.66 14.9 最大时间 28.46 20.56 27.7 72 平均时间 17.21 12.20 29.1 最大时间 37.33 20.14 46.0 表 6 双移线工况横向偏差对比
Table 6. Comparison of lateral deviation for the double-shift-line working condition
车速/
(km·h−1)指标 控制器
1/m控制器
2/m改善
程度/%36 平均偏差 0.086 0.062 27.9 最大偏差 0.509 0.388 23.8 54 平均偏差 0.084 0.072 14.3 最大偏差 0.658 0.469 28.7 72 平均偏差 0.125 0.107 14.4 最大偏差 0.740 0.517 30.1 表 7 双移线工况横摆角偏差对比
Table 7. Comparison of yaw angle deviation for the double-shift-line working condition
车速/
(km·h−1)指标 控制器1/rad 控制器2/rad 改善程度/% 36 平均偏差 0.013 0.010 23.1 最大偏差 0.078 0.058 25.6 54 平均偏差 0.015 0.011 26.7 最大偏差 0.084 0.069 17.9 72 平均偏差 0.018 0.013 27.8 最大偏差 0.090 0.073 18.9 -
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